The basics of atoms

How do atoms work and what shape do they have ?

For a quick overview (like here) a detailed understanding of the inner workings of atoms is not (yet) necessary. For more detailed analysis (later) a detailed understanding is absolutely indispensable. If you want to dive down a bit further right away then check out the main article: "The nature and shape of atoms"

The focus here will be mostly limited on the lightest simplest most common (and most APM relevant) elements at the upper end of the periodic table.

Tetrapodal arrangement of electron clouds

Tetrapodal electron cloud arrangement (tech term: sp³) Note: This is still a simplified view. The orbitals are actually more bean shaped, overlapping and blurry. But depicting it more realistically would obfuscate the geometric arrangement too much.

In those most common elements the most common arrangement of the outer (and thus relevant) "electron clouds" (in molecules or crystals) is tetrapodal (tetrahedral) with four lobes (four==tetra). As depicted in blue here. Note that the small lobes are part of the big ones on the opposing side respectively.

A more technical term for "electron clouds" is "orbitals" specifically the ones depicted blue here are called "hybrid orbitals".

• Orbitals filled with two electrons from the host atom (as depicted here) are called "lone pairs" and repel lone pairs from other atoms.
• Orbitals filled with one electron from the host atom and one electron from a neighboring atoms merge together and are called bonding "molecular orbitals".
• In case too many electrons are missing (sometimes the case with elements to the left of carbon in the periodic table) the geometric arrangement of electron clouds can change. Details elsewhere.

The four orbitals in the tetropodal geometry do not lie in a common plane (they are not coplanar) In case one has just the right amount of electrons:

• not too many - forming lone pairs
• not too few - changing orbital arrangement

... like in the case of carbon (and silicon) then the atoms can bond to other atoms in all four non coplanar directions and can form three dimensional crystal structures. Not just sheets or chains. The prime examples for tightly meshed 3D networks of that kind are diamond and silicon (silicon-the-crystal not silicon-the-element). This is one of the reasons why carbon is sometimes referred to as "king of elements".

Triangular arrangement of hybrid orbitals

Triangular electron cloud arrangement. (tech term: sp²) Note: the fourth orbital is not depicted!

There are other possible electron cloud arrangements too. The second most common one is triangular (as depicted here in blue).

The light elements have four outer shell orbitals but only three are depicted here, so one is obviously missing. The missing/non-depicted fourth one sticks out vertically both up and down equally from the image-plane. The fourth orbital has no small and big lobe like the three depicted hybrid orbitals have. It is a fundamental orbital (a p-orbital - a raw solution from the underlying math) with two lobes of exactly equal size.

The three hybrid orbitals lie in the same plane and the fourth (the fundamental) orbital has no preference for facing upwards or downwards. Thus atoms that take on this triangular orbital arrangement cannot form three dimensional structures in a way like the atoms with tetrapodal structure. Instead they can only form two dimensional sheets.

Just like in the tetrapodal arrangement also in the triangular arrangement case carbon (and silicon) atoms have the ideal number of electrons to neither form lone pairs (repulsing other lone pairs) nor change orbital arrangement. Thus a prime example for sheets out of atoms in triangular orbital arrangement are sheets made out of carbon.

In the simplest, that is fully planar, form this is called a graphene sheet. Stacks of large graphene sheets form very hard single crystalline graphite. Normal pencil mine graphite is polycrystalline allowing the small sheet-flakes to slide over each other making it very soft. (Side-note: Larger chunks of single crystalline graphite do not occur naturally but can by synthesized today. It is called: HOPG)

In a graphene sheet the fourth orbital (the non-hybridized fundamental p-orbital) different from the three triangularly arranged hybrid orbitals plays a very special role. Not only sticks it out both sides equally it also shares one bond in three directions simultaneously on each side. All those doublesided p-prbitals fuse together to one single giant (double sheeted) molecule orbital spanning over the whole sheet on both sides. This allows electrons to move freely (electric conductivity).

Bending graphite sheets by various means can drastically (and usefully) change the electronic properties. From semi-conductivity to very high conductivity (much better than copper or silver).

The tech term for hybrid orbitals that assume the here describesd triangular shape is: sp².

Beside electronic property changes bending sp² sheets (graphite or other) also allows them to form three dimensional structures when the sheets locally can actually only be two dimensional.

• Flat sheets must have all atoms arranged in hexagons.
• Flat sheets occur rolled up into tubular shapes (Nanotubes in general). Beside various diameters different rolling angles are possible (causing different eletronic properties).
• Sheets can be bent convex (or concave depending on the onlooking side) by replacing some hexagons with pentagons, squares or even triangles (Buckyballs in general).
• Sheets can be bent hyperbolic by replacing some hexagons with heptagons, octagons, ... (Foam like structures e.g. DLC)